Three-flavor oscillation probabilities P(νₐ→νᵦ) via mixing matrix
Oscillation Probabilities vs L/E
PMNS Matrix |U_αi|²
P(νₑ→νₑ) + P(νₑ→νμ) + P(νₑ→ντ) = 1.000
Three-flavor oscillation: P(νₐ→νᵦ) = |Σᵢ Uₐᵢ U*ᵦᵢ exp(−iΔm²ᵢ₁L/4E)|².
The PMNS matrix U = R₂₃·R₁₃(δ)·R₁₂ parameterizes mixing between flavor and mass eigenstates.
Observed values (NuFIT 2023): θ₁₂≈33.5°, θ₂₃≈42°, θ₁₃≈8.5°, δ_CP≈221°.
L/E in km/GeV (natural units with ℏc=197 MeV·fm): oscillation length L_osc = 4πE/Δm².
Matter effects (MSW): electron neutrinos interact with electrons; effective mass in matter modifies oscillations.